Mix together graham cracker crumbs, melted butter, cinnamon, and nutmeg in a bowl.
Press the mixture into an 8-inch pie dish. Refrigerate while making filling.
Beat cream cheese in a mixing bowl with an electric mixer on medium speed until softened. reduce the speed to low, and gradually beat in milk, a little at a time (mixture will be watery). Use a rubber spatula to scrape cream cheese from the sides of the bowl, if necessary.
Beat in pudding mix until the filling is thick and smooth.
Spoon half of the cream cheese filling into the bottom of the graham cracker crust.
Spread half the strawberries over the filling.
Repeat cheesecake layer and strawberry layer.
Chill pie in refrigerator until set and cold, at least 1 hour.